The inverse of the real function f x -4 x -3 x -4- x -4-3- is f -1 x -A- 3 x-3-4 xB- 4 x-4-3 x- 4 x-3-4 xD- 3 x-4-3 x

The correct option is B y = f(x) = 4x/3x+4⇒ x =4y/4 3y⇒ f^ 1 (x) =4x/4 3x ...

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Standard XII

Mathematics

Theorems for Continuity

The inverse o...

Question

The inverse of the real function f(x) = $\frac{4 x}{3 x + 4}$ , $x \neq \frac{- 4}{3}$ ,is f^-1(x) =

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Solution

The correct option is B

y = f(x) = $\frac{4 x}{3 x + 4} \Rightarrow x = \frac{4 y}{4 - 3 y} \Rightarrow f^{- 1} (x) = \frac{4 x}{4 - 3 x}$

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Similar questions

Q. Let

f : R - {- \frac{4}{3}} \to R

be a function defined as

f (x) = \frac{4 x}{3 x + 4}

. The inverse of

f

is the map

g : R a n g e f \to R - {- \frac{4}{3}}

given by

Consider $f : R - {- \frac{4}{3}} \to R - {\frac{4}{3}}$ given by $f (x) = \frac{4 x + 3}{3 x + 4}$ .Show that f is bijective.Find the inverse of f and Hence find $f^{- 1} (0)$ and x such that $f^{- 1} (x) = 2$ .

Q. Solve :

\frac{4 + 3 x}{4 - 3 x} + \frac{3 + 4 x}{3 - 4 x} = 0

Q. Consider

f : R - {- \frac{4}{3}} \to R - {\frac{4}{3}}

given by

f (x) = \frac{4 x + 3}{3 x + 4}

. Show that

f

is bilective. Find the inverse of

f

and hence find

f^{- 1} (0)

and

x

such that

f^{- 1} (x) = 2

Q. Consider

f : R - {- \frac{4}{3}} \to R - {\frac{4}{3}}

given by

f (x) = \frac{4 x + 3}{3 x + 4}

. Show that

f

is bilective. Find the inverse of

f

and hence find

f^{- 1} (0)

and

x

such that

f^{- 1} (x) = 2

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The inverse of the real function f(x) = 4x3x+4 , x≠−43,is f -1(x) =

The correct option is B y = f(x) = 4x3x+4⇒x=4y4−3y⇒f−1(x)=4x4−3x

The inverse of the real function f(x) = $\frac{4 x}{3 x + 4}$ , $x \neq \frac{- 4}{3}$ ,is f^-1(x) =

The correct option is B

y = f(x) = $\frac{4 x}{3 x + 4} \Rightarrow x = \frac{4 y}{4 - 3 y} \Rightarrow f^{- 1} (x) = \frac{4 x}{4 - 3 x}$